Nuprl Lemma : list-if-has-value-list_ind
∀b,f:Base.
∀l:Base. l ∈ Base List supposing (rec-case(l) of [] => b | a::b => r.f[a;r])↓ supposing ∀x:Base. strict(λu.f[x;u])
Proof
Definitions occuring in Statement :
list_ind: list_ind,
list: T List,
strict: strict(F),
has-value: (a)↓,
uimplies: b supposing a,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
member: t ∈ T,
lambda: λx.A[x],
base: Base
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
list_ind: list_ind,
uall: ∀[x:A]. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
guard: {T},
prop: ℙ,
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
top: Top,
not: ¬A,
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
subtract: n - m,
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
nat_plus: ℕ+,
has-value: (a)↓,
so_lambda: λ2x.t[x],
so_apply: x[s],
cons: [a / b],
strict: strict(F),
cand: A c∧ B,
it: ⋅,
nil: []
Lemmas referenced :
nil_wf,
has-value-implies-dec-isaxiom-2,
cons_wf,
strict_wf,
all_wf,
base_wf,
top_wf,
has-value-implies-dec-ispair-2,
fun_exp_unroll_1,
le-add-cancel,
add-zero,
add_functionality_wrt_le,
add-commutes,
add-swap,
add-associates,
minus-minus,
minus-add,
minus-one-mul-top,
zero-add,
minus-one-mul,
condition-implies-le,
less-iff-le,
not-ge-2,
false_wf,
subtract_wf,
decidable__le,
bottom_diverge,
strictness-apply,
fun_exp0_lemma,
int_subtype_base,
has-value_wf_base,
less_than_wf,
ge_wf,
less_than_irreflexivity,
less_than_transitivity1,
nat_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
sqequalRule,
hypothesis,
compactness,
thin,
lemma_by_obid,
isectElimination,
hypothesisEquality,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
independent_functionElimination,
voidElimination,
lambdaEquality,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
because_Cache,
isect_memberEquality,
voidEquality,
unionElimination,
independent_pairFormation,
productElimination,
addEquality,
intEquality,
minusEquality,
dependent_set_memberEquality,
callbyvalueCallbyvalue,
callbyvalueReduce
Latex:
\mforall{}b,f:Base.
\mforall{}l:Base. l \mmember{} Base List supposing (rec-case(l) of [] => b | a::b => r.f[a;r])\mdownarrow{}
supposing \mforall{}x:Base. strict(\mlambda{}u.f[x;u])
Date html generated:
2016_05_14-AM-06_33_24
Last ObjectModification:
2016_01_14-PM-08_25_24
Theory : list_0
Home
Index